I know that the figures and tables are numbered consecutively throughout the
while paper. What about the equation numbering? Suppose I have four equations in the paper, but I want to number only two of them. Is it appropriate to do it?

In general, for technical subjects, number all equations even though you may not have referenced them in the text. It is almost always recommended that you do so, so that other people can refer to it easily and also so that any queries that are asked regarding it, can be directly done. For example, if you have two unnumbered equations and your reader has a question regarding one of them, there is no way for them to do so (they would have to be ambiguous...that equation that appears after this paragraph, which is something most of us would not like to do (and not preferable in an academic setting). So, in general, go ahead and number all of them.

When you write a paper, you normally want to show the derivation of your mathematical results. Every step should be numbered. Then it is up to you to mention them or not in the text. LaTeX (TeX Stack Exhange) does the numbering automatically for you!